This invention relates to coherent anti-Stokes Raman spectroscopy and more particularly to crossed-beam coherent anti-Stokes Raman spectroscopy.
Coherent anti-Stokes Raman spectroscopy (CARS) offers very promising potential for the diagnostic probing of high interference environments such as those typical of combustion processes and electric discharges. In CARS systems, incident laser beams at frequencies .omega..sub.1 and .omega..sub.2 interact through the third order non-linear susceptibility .chi..sup.(3) (-.omega..sub.3, .omega..sub.1, .omega..sub.1, -.omega..sub.2) to generate a polarization component which produces coherent radiation at frequency .omega..sub.3 equal to 2 .omega..sub.1 -.omega..sub.2. When the frequency difference .omega..sub.1 -.omega..sub.2 is close to the frequency of a Raman active resonance, .omega..sub.Raman, within the environment being probed, the magnitude of the radiation at .omega..sub.3, which is then at the anti-Stokes frequency relative to .omega..sub.1, can become very large. The incident beams, that is .omega..sub.1 and .omega..sub.2 must be aligned so that the three wave mixing process is properly phased. Phase matching requires that 2K.sub.1 =K.sub.2 +K.sub.3 where K.sub.i is the wave vector at frequency .omega..sub.i with absolute magnitude equal to .omega..sub.i n.sub.i /c where c is the speed of light and n.sub.i is the refractive index at a frequency .omega..sub.i. For gases which are nearly dispersionless, phase matching occurs when the beams are collinearly mixed. Although this is easy to implement, collinear phase matching possesses a number of drawbacks from a diagnostic standpoint. In particular, since the CARS signal is coherent and represents an integrative effect, the spatial resolution cannot be well defined by imaging techniques, such as those successfully employed in spontaneous Raman approaches, to yield very fine spatial resolution. Collinear phase matching can result in poor and often ambiguous spatial resolution.
Since the CARS signal strength scales as the intensity product I.sub.1.sup.2 I.sub.2, where I.sub.1 is the intensity of a beam at .omega..sub.1 and I.sub.2 is the intensity of the beam at .omega..sub.2, the incident laser beams are generally focused for diagnostic purposes when collinear phase matching is employed. For diffraction-limited beams, the interaction is assumed to occur primarily within a cylindrical volume of diameter v and length 6l given by the expression v=4.lambda.f/II D and l is equal to IIv.sup.2 /2.lambda. where f is the focusing lens focal length, D is the beam diameter at the lens and .lambda. is the wavelength. As shown in Table 1 the probe volume focal diameter, the cross-sectional area, and the length are tabulated for various focal length lenses for a 1 centimeter diameter beam at 5320 A. Depending upon the specific diagnostic circumstances, i.e. the focusing lens to measurement point separation, the spatial resolution may exceed that which is desired. Although the resolution is very good for short focal length lenses, gas breakdown may limit the input beam intensities and greatly diminish the CARS signal level. Additionally, many laser beams are not diffraction-limited, resulting in much poorer spatial resolution than that tabulated in Table 1. For example for a "three times diffraction-limited" beam divergence angle, the linear resolution would be about an order of magnitude poorer. In the presence of density gradients, the resolution may further degrade since the CARS power also scales as a power of the gas density, typically the power being between 1 to 2. Also for specific applications, such as probing a flame in a burner operating at atmospheric pressure, significant contributions to the CARS signal may originate from cold, high density gas regions adjacent to the flame. Furthermore CARS signal contributions may be generated from various elements within the optical train, for example, the lenses and filters, when collinear phase matching is utilized. These contributions could be significant when low gas densities or weak resonances are being probed. Clearly it is desirable to avoid beam overlap and potential three wave mixing in all regions except the desired measurement location.
In an attempt to avoid collinearity, the .omega..sub.1 and .omega..sub.2 beams can be introduced at a slight angle to one another. As phase mismatch is deliberately introduced in this manner, the CARS signal generating efficiency will drop. For example at .DELTA.K1.apprxeq.3 where .DELTA.K is the magnitude of the phase mismatch, i.e. .vertline.2K.sub.1 -K.sub.2 -K.sub.3 .vertline. the CARS efficiency will have decreased by an order of magnitude. Although one could operate in this manner it is clearly inefficient and the actual spatial resolution will depend very critically on the precise angular separation of the beams.